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1) integral ∫x/(1+x) dx vs 2) integral ∫sin(x) cos(x)/(1+ sin(x)) dx
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
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Review: Linear form, Quadratic form & Bilinear form
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2nd way: integral ∫ log √x(x^n) dx
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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx
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UC Davis #3 2nd way: ∫(2-x)/(x^2+5x)dx [integration by partial fraction]
5 ways: integral ∫a^(px+q) dx
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How many words, with or withOUT meaning, each of 3 vowels & 2 consonents ...
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UC Davis #1 2nd way: integral ∫1/(x^2-4) dx [integration by partial fraction]
exp integral ∫1/(e^(2x) - 25) dx
alternate way: ∫ √(x^2+a^2 )dx via "expressing in 2 ways"
2nd way: integral ∫x^k ln(x) dx = x^(k+1)/(k+1) ln(x) - x^(k+1)/(k+1)^2 + C where C ≠ -1
NUS MA1102R: Find ALL second-order partial derivatives of f(x,y) = x^2 y -y^3 + ln(x)
prob stat: A die with 4 red faces & 2 green faces is rolled twice.
2nd/2 parts: Mean 1+2+3+...+n is just (1+n)/2. Why?
JEE Main integral x^2/(a+bx)^2 dx
Review: Arithmetic Series a+(a+d)+(a+2d)+...+(a+(n-1)d)=
2nd way: sq rt integral ∫(√x)/(x+1) dx
2nd/3 ways: How many chords can be drawn through 21 points on a circle?